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		<P class='majorTitle'>com.wis.math.geom.util.Graphic Documentation</P>


		<P><B>Author:</B> <a href='mailto:wisolutions2002@shaw.ca?subject=wisASLibrary Graphic Class'>Richard Wright</a><BR>
		<B>Last Modified:</B> 07/08/05 15:08:20<HR class='big'>

		<P class='sectionTitle'>Summary</P>
		<P class='ToC'>com.wis.math.geom.util.Graphic class:</P>
		<div class='methodsDiv'><a href='#classinfo'>- description</a></div>
<P class='ToC'>com.wis.math.geom.util.Graphic Properties:</P><div class='methodsDiv'>
<a href='#none'>- none</a><br>
</div><br>
<P class='ToC'>com.wis.math.geom.util.Graphic Methods:</P><div class='methodsDiv'>
<a href='# distance'>-  distance</a><br>
<a href='# angle'>-  angle</a><br>
<a href='# radAngle'>-  radAngle</a><br>
<a href='# toStandardAngle'>-  toStandardAngle</a><br>
<a href='# lineToStandardAngle'>-  lineToStandardAngle</a><br>
<a href='# angleSpan'>-  angleSpan</a><br>
<a href='# averageAngle'>-  averageAngle</a><br>
<a href='# numSort'>-  numSort</a><br>
<a href='# toPoint'>-  toPoint</a><br>
<a href='# toPolar'>-  toPolar</a><br>
<a href='# intersectLines'>-  intersectLines</a><br>
<a href='# intersectLinesImplicit'>-  intersectLinesImplicit</a><br>
<a href='# intersectLinesParametric'>-  intersectLinesParametric</a><br>
<a href='# distPtSegment'>-  distPtSegment</a><br>
<a href='# getMiddle'>-  getMiddle</a><br>
<a href='# pointOnSegment'>-  pointOnSegment</a><br>
<a href='# isPointOnSegment'>-  isPointOnSegment</a><br>
<a href='# projectDistance'>-  projectDistance</a><br>
<a href='# triangleArea'>-  triangleArea</a><br>
<a href='# polygonArea'>-  polygonArea</a><br>
<a href='# parabolaArcLength'>-  parabolaArcLength</a><br>
<a href='# dms2Deg'>-  dms2Deg</a><br>
<a href='# deg2Dms'>-  deg2Dms</a><br>
<a href='# convertDeg'>-  convertDeg</a><br>
<a href='# convertRad'>-  convertRad</a><br>
<a href='# convertMultPI'>-  convertMultPI</a><br>
<a href='# convertDms'>-  convertDms</a><br>
</div><br>

		<HR class='big'>
		<P class='sectionTitle'><A name='classinfo'></A>com.wis.math.geom.util.Graphic <I>class</I></P>
		<P> <span class='methodTitle'>version:</span> 1.8</P>
		<P class="methodTitle">description:</P>
		<P>Implements the static behaviours of the Graphic Class.
 		Provides methods for the geometric manipulation of the screen graphics.
 </P>
		<P class="methodTitle">usage:</P> <pre>Graphic.classMethod(args);</pre>

<P> <span class='methodTitle'>parameters:</span>
				<ul>
<li>      none  -- no class input parameters.</li>
</ul>

			<HR class='small'>
			<P class='groupTitle'><A name='properties'></A>com.wis.math.geom.util.Graphic Properties:</P>
			<div class='methodsDiv' >


				<P class='methodTitle'><A name='none'></A><u> none</u></P>
				<P> -- no class properties.</P>
</div>

			<HR class='small'>
			<P class='groupTitle'><A name='methods'></A>com.wis.math.geom.util.Graphic Methods:</P>
			<div class='methodsDiv' >


				<P class='methodTitle'><A name=' distance'></A><u>  distance</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines the distance between two Point objects.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.distance(p1,p2);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  p1   (Point)  -- a point object in 2 or 3-space.</li>
<li>  p2   (Point)  -- a point object in 2 or 3-space.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns total distance between 2 points.
    </P>

				<P class='methodTitle'><A name=' angle'></A><u>  angle</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines the angle in degrees of the line between two Point
     objects wrt the positive x-axis.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.angle(p1,p2);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  p1   (Point)  -- a point object in 2-space.</li>
<li>  p2   (Point)  -- a point object in 2-space.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns angle of line in degrees (-180° to 180°).
    </P>

				<P class='methodTitle'><A name=' radAngle'></A><u>  radAngle</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines the angle in radians of the line between two Point
     objects wrt the positive x-axis.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.radAngle(p1,p2);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  p1   (Point)  -- a point object in 2-space.</li>
<li>  p2   (Point)  -- a point object in 2-space.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns angle of line in radians (-PI to PI).
    </P>

				<P class='methodTitle'><A name=' toStandardAngle'></A><u>  toStandardAngle</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Changes a Flash angle (-180° to 180°) into standard
     angle (0° to 360° CCW) wrt the positive x-axis using
     angle input.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.toStandardAngle(ang);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  ang   (Number)  -- an angle in degrees (-180° to 180°).</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns an angle in degrees (0° to 360° CCW).
    </P>

				<P class='methodTitle'><A name=' lineToStandardAngle'></A><u>  lineToStandardAngle</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Changes a Flash angle (-180° to 180°) into standard
     angle (0° to 360° CCW) wrt the positive x-axis using
     point object input.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.lineToStandardAngle(p1,p2);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  p1   (Point)  -- a point object in 2-space.</li>
<li>  p2   (Point)  -- a point object in 2-space.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns an angle in degrees (0° to 360° CCW).
    </P>

				<P class='methodTitle'><A name=' angleSpan'></A><u>  angleSpan</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines the difference in degrees of two angles with span
     based on Boolean input.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.angleSpan(ang1,ang2,cw);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  ang1   (Number)  -- a start angle in degrees.</li>
<li>  ang2   (Number)  -- an end angle in degrees.</li>
<li>  cw   (Boolean)  -- optional, measures clockwise if true, counter-clockwise if false.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns the difference between 2 angles in degrees.
    </P>

				<P class='methodTitle'><A name=' averageAngle'></A><u>  averageAngle</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines the average angle for input of an array of angles.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.averageAngle(arr);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  arr   (Array)  -- an array of angle in degrees.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns the average of all angles.
    </P>

				<P class='methodTitle'><A name=' numSort'></A><u>  numSort</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Dependent sort by number method for 'averageAngle' sort above.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.numSort(a,b);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  a   (Number)  -- any real number.</li>
<li>  b   (Number)  -- any real number.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns two input numbers sorted min to max.
    </P>

				<P class='methodTitle'><A name=' toPoint'></A><u>  toPoint</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines Vector cartesian coordinates in 2-space -- expects to be
     passed: {a:n,r:n} (angle & radius).
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.toPoint(vecObj );</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  vecObj   (Object)  -- a vector object -- {a:n,r:n} (angle & radius).</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Point)  -- returns an object containing Vector Cartesian coordinates.
    </P>

				<P class='methodTitle'><A name=' toPolar'></A><u>  toPolar</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines Vector polar coordinates in 2-space -- expects to be
     passed: {x:n,y:n}.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.toPolar(vec);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  vec   (Vector)  -- a Vector object -- {x:n,y:n}.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Object)  -- returns an object containing Vector polar coordinates.
    </P>

				<P class='methodTitle'><A name=' intersectLines'></A><u>  intersectLines</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines an intersection point of two lines in 2-space
     using the explicit line equation:
     <blockquote><pre>
     y = f(x) = mx + b
     </pre></blockquote>
     Contains a 2D vertical work-around to clip slopes
     measured to infinity.<br>
     Expects to be passed two: line object = {p1:Point,p2:Point}
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.intersectLines(l1,l2);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  l1   (Object)  -- line object containing 2 Point objects.</li>
<li>  l2   (Object)  -- line object containing 2 Point objects.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Point)  -- returns a Point object for the line intersection point.
    </P>

				<P class='methodTitle'><A name=' intersectLinesImplicit'></A><u>  intersectLinesImplicit</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines an intersection point of two lines in 2-space
     using the implicit line equation:
     <blockquote><pre>
     f(x,y) = ax + by + c = 0
     </pre></blockquote>
     Expects to be passed two: line object = {p1:Point,p2:Point}
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>
     Graphic.intersectLinesImplicit(l1,l2);
     // which in turn calls:
     var t1:Intersect2DLine = new Intersect2DLine();
     var t2:Intersect2D = t1.lineLine(l1.p1,l1.p2,l2.p1,l2.p2);
     var pt:Point = new Point(t2.$points[0].x,t2.$points[0].y);
     </pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  l1   (Object)  -- line object containing 2 Point objects.</li>
<li>  l2   (Object)  -- line object containing 2 Point objects.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Point)  -- returns a Point object for the line intersection point.
    </P>

				<P class='methodTitle'><A name=' intersectLinesParametric'></A><u>  intersectLinesParametric</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines in 3-space either an intersection point of two lines, or else the
     more common case, the shortest path to the nearest point of each line,
     using the parametric line equation:
     <blockquote><pre>
     P(t) = P0 + tvL
     </pre></blockquote>
     Expects to be passed two: line object = {p1:Point,p2:Point}
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.intersectLinesParametric(l1,l2[,true]);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  l1   (Object)  -- line object containing 2 Point objects.</li>
<li>  l2   (Object)  -- line object containing 2 Point objects.</li>
<li>  bSeg  (Boolean)  -- clamps calculation to line segments if passed true.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Point)  -- returns a Point object for the line intersection point.
    </P>

				<P class='methodTitle'><A name=' distPtSegment'></A><u>  distPtSegment</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines shortest distance between a point and a
     line segment in 3-space.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.distPtSegment(P,S);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  P   (Point)  -- an object defining a point in 3-space.</li>
<li>  S   (Object)  -- an object defining end Point objects for</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns shortest distance value.
    </P>

				<P class='methodTitle'><A name=' getMiddle'></A><u>  getMiddle</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines the midpoint between two Point objects.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.getMiddle(p1,p2);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  p1   (Point)  -- a start Point object.</li>
<li>  p2   (Point)  -- an end Point object.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Point)  -- returns a new Point object.
    </P>

				<P class='methodTitle'><A name=' pointOnSegment'></A><u>  pointOnSegment</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines a point on a line segment based on a scalar.
	 </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.pointOnSegment(p1,p2,ratio);</pre>
	 </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  p1   (Point)  -- a start Point object.</li>
<li>  p2   (Point)  -- an end Point object.</li>
<li>  ratio   (Number)  -- a scalar (0 - 1).</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Point)  -- returns a new Point object.
	</P>

				<P class='methodTitle'><A name=' isPointOnSegment'></A><u>  isPointOnSegment</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Tests whether all three passed Point objects lie on the same
     line sgment, and whether p3 lies between p1 and p2.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.isPointOnSegment(p1,p2,p3);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  p1   (Point)  -- a start Point object.</li>
<li>  p2   (Point)  -- an end Point object.</li>
<li>  p3   (Point)  -- a Point object to test for line intercept.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Boolean)
    </P>

				<P class='methodTitle'><A name=' projectDistance'></A><u>  projectDistance</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Defines projected distance between two Point objects.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.projectDistance(p1,p2);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  p1   (Point)  -- a start Point object.</li>
<li>  p2   (Point)  -- an end Point object.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns total projected distance.
    </P>

				<P class='methodTitle'><A name=' triangleArea'></A><u>  triangleArea</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Calculates triangle area.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.triangleArea(p1,p2,p3);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  p1   (Point)  -- a vertex Point object.</li>
<li>  p2   (Point)  -- a vertex Point object.</li>
<li>  p3   (Point)  -- a vertex Point object.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns area for the triangle.
    </P>

				<P class='methodTitle'><A name=' polygonArea'></A><u>  polygonArea</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Calculates the area of a convex or concave,
     non-self-intersecting polygon.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.polygonArea(arr);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  arr   (Array)  -- an array of vertex Point objects.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns area for the polygon.
    </P>

				<P class='methodTitle'><A name=' parabolaArcLength'></A><u>  parabolaArcLength</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Calculates the length of a parabola.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.parabolaArcLength(a,b);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  a   (Number)  -- length measure of the parabola's point projection (N <-> S).</li>
<li>  b   (Number)  -- length measure of the parabola's point projection (E <-> W).</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns the total length of the parabola.
    </P>

				<P class='methodTitle'><A name=' dms2Deg'></A><u>  dms2Deg</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Converts a string with degrees[:minutes[:seconds]] to decimal degrees.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.dms2Deg(sDms);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  sDms   (String)  -- a string with degrees[:minutes[:seconds]].</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns a decimal number for degrees.
    </P>

				<P class='methodTitle'><A name=' deg2Dms'></A><u>  deg2Dms</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Converts decimal degrees to a deg:min:sec string.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.deg2Dms(deg);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  deg   (Number)  -- a real number for degrees.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (String)  -- returns a string representation for degrees[:minutes[:seconds]].
    </P>

				<P class='methodTitle'><A name=' convertDeg'></A><u>  convertDeg</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Converts an angle in degrees to a string output.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.convertDeg(deg,sOut);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  deg   (Number)  -- a real number for degrees.</li>
<li>  sOut   (String)  -- a string passed to target output string type.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (String)  -- returns a string representation of  'dms', 'rad', or 'multPI'.
    </P>

				<P class='methodTitle'><A name=' convertRad'></A><u>  convertRad</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Converts radian input to a string output.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.convertRad(rad,sOut);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  rad   (Number)  -- a real number for radians.</li>
<li>  sOut   (String)  -- a string: 'dms', 'deg', or 'multPI'.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (String)  -- returns a string representation of  'dms', 'deg', or 'multPI' output.
    </P>

				<P class='methodTitle'><A name=' convertMultPI'></A><u>  convertMultPI</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Converts multPI input to a string output.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.convertMultPI(multPI,sOut);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  multPI   (Number)  -- a real number for multPI</li>
<li>  sOut   (String)  -- a string: 'dms', 'deg', or 'rad'.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (String)  -- returns a string representation of 'dms', 'deg', or 'rad' output.
    </P>

				<P class='methodTitle'><A name=' convertDms'></A><u>  convertDms</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Converts dms input to a string output.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>Graphic.convertDms(sDms,sOut);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  sDms   (String)  -- a string representation  for dms.</li>
<li>  sOut   (String)  -- a string: 'multPI', 'deg', or 'rad'.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns a real number for 'multPI', 'deg', or 'rad' output..
    </P>
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